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STAT 3502
Assignment # 4
Total mark=25
Due: 9 August, 2010 prior to the start of class
1. Suppose that a random sample of size
n
is drawn from the Bernoulli distribution
f
(
x
;
p
) =
(
p
x
(1

p
)
1

x
x
= 0
,
1
0
otherwise.
Find a maximum likelihood estimator of
p
.[3]
2. In a survey of 4720 American, 708 of them were overweight. calculate and interpret a 99% conﬁdence
interval for the proportion of all American who are overweight.[3]
3. For a sample of 69 healthy trees, the sample mean of dyelayer density was 1.028 and the sample
standard deviation was 0.163.
a.
Calculate a 95% CI for the true average dyelayer density for all such trees.[2]
b.
Suppose the investigators had made a rough guess of 0.16 for the value of
σ
before collecting
data. What sample size would be necessary to obtain an interval width of 0.05 for a conﬁdence level
of 95%?[2]
4. Consider a random sample
X
1
,
···
,X
n
from a pdf
f
(
x
;
θ
) = 0
.
5(1 +
θx
)

1
≤
x
≤
1
,

1
≤
θ
≤
1
show that
ˆ
θ
= 3
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 Spring '09
 JHONBRAN

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